勷勤数学•专家报告

题      目：$H^{\frac{7/4}}$ ill-posedness of the compressible ideal MHD system in 2D

报  告  人：尹思露 副教授  (邀请人：罗天文)

                                             杭州师范大学

时      间：6月20日  16：30-17：30

地     点：数科院西楼114

报告人简介:

       尹思露，杭州师范大学副教授。博士毕业于复旦大学数学系，师从周忆教授。主要研究双曲型偏微分方程解的适定性及奇性理论。在Amer. J. Math、SIAM JMA、JDE等杂志发表多篇论文。

摘      要：

       In this talk, we investigate the ill-posedness of the non-strictly hyperbolic compressible ideal MHD (IMHD) system in two dimensions, which exhibits multiple propagation speeds. For scalar quasilinear wave equation, Smith-Tataru showed its local well-posedness in $H^{\frac{11/4}+} \times H^{\frac{7/4}+}$. Here, we construct a counterexample to the local existence of low-regularity solutions to the IMHD system in the borderline space $H^{\frac{7/4}}$. Our proof is based on a coalition of a carefully designed algebraic approach and Christodoulou’s geometric approach. We give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on a joint work with Xinliang An (NUS) and Haoyang Chen (NUS).

          欢迎老师、同学们参加、交流！